Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition...

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Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem Law of Cosines Resolving Components Angle of a Resultant: tan -1 Θ Problem page 75

Transcript of Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition...

Page 1: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Day 14, Tuesday, 15 September, 2015Vector Problems

Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem Law of Cosines Resolving Components Angle of a Resultant: tan-1 Θ Problem page 75

Page 2: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

In summary: In an equation or operation with a scalar or dot

product, the answer is a scalar quantity that is the product of two vectors.

The dot product is found by multiplying the components of vectors that are in the same direction.

ABcosΘ In an equation or operation with a vector or

cross product, the answer is a vector quantity that is the product of two vectors.

The cross product is found by multiplying the components of vectors that are perpendicular to each other.

ABsinΘ

Page 3: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Vocabulary

Speed is a scalar with magnitude only

Velocity is a vector with magnitude

and direction

w r t means with respect to

Page 4: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Lecture- Vectors Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem Law of Cosines Resolving Components Angle of a Resultant: tan-1 Θ Problem page 75

Page 5: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Graphical representation

Arrows Can slide around Cannot change direction Cannot change length Add tip to tail

Page 6: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Resultant

Page 7: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Addition

Page 8: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Addition of several vectors

Page 9: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Subtraction

Page 10: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Reference Angle

Always in Quadrant I

Page 11: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Sin, Cos, Tan

Sine = sin = opp/hyp

Cosine = cos = adj/hyp

Tangent = tan = sin/cos = opp/adj

Page 12: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Complimentary Angles

Complimentaryangles makeother anglesfeel goodabout themselves

Page 13: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Pythagorean Theorem

R2 = A2 + B2

Works only for 90º angle

Page 14: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Pythagorean Theorem

Page 15: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Law of Cosines

R2 = A2 + B2 – 2AB cos Θ

Works for any angle

Page 16: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Resolving Components

x = r cos Θ

y = r sin Θ

Page 17: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Angle of a Resultant:

tan-1 Θ

Page 18: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Typical Vector Problems

1. Walking home

2. Boat on a river

3. Three vectors

Page 19: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Chapter 3 Problems

Page 20: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Credits

Reference Angle www.netcomuk.co.u

Complimentary Angles Cartoon www.cartoonstock.com

Vector Addition and Subtraction Wikipedia

Page 21: Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

Credits II

Vector Sliding and Multiple Additions www.physics.uoguelph.ca

Resultant www.mathwarehouse.com


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